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## Arithmetic: Simple Interest Test -5

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Question 1 |

A person invested some amount at the rate of 12% simple interest and a certain amount at the rate of 10% simple interest. He received yearly interest of Rs130. But if he had interchanged the amounts invested, he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest?

Rs 700 | |

Rs 500 | |

Rs 800 | |

Rs 400 |

Question 1 Explanation:

Amount invested at 12% = Rs A

Amount invested at 10% = Rs B

=> 130 =(A x 12 x1 )/100 +(B x 10 x1 )/100

=> 13000 =12A + 10B............................................................1

=> 134 =(A x 10 x1 )/100 +(B x 12 x1 )/100

=>13400 = 10A + 12B..............................................................2

Solving equations 1 and 2 we get

A = Rs 500

So the amount invested at the rate of 12% is Rs 500

Amount invested at 10% = Rs B

=> 130 =(A x 12 x1 )/100 +(B x 10 x1 )/100

=> 13000 =12A + 10B............................................................1

=> 134 =(A x 10 x1 )/100 +(B x 12 x1 )/100

=>13400 = 10A + 12B..............................................................2

Solving equations 1 and 2 we get

A = Rs 500

So the amount invested at the rate of 12% is Rs 500

Question 2 |

A money lender lent out Rs 25000 in two parts, one at 8% and the other at 8.5%. If the total annual income on the amount is Rs 2031.25, the money lent at 8% is?

Rs 12500 | |

Rs 6250 | |

Rs 10000 | |

Rs 18750 |

Question 2 Explanation:

Total money = Rs 25000

Let the amount which is lent is A at 8%

Therefore the other part which is at 8.5% = (25000 â€“ A)

Therefore (A x 8 x 1)/100 + {(25000 â€“ A) x 8.5 x 1}/100 = 2031.25

=> 8A + 212500 - 8.5A = 203125

=> A= Rs 18750

Let the amount which is lent is A at 8%

Therefore the other part which is at 8.5% = (25000 â€“ A)

Therefore (A x 8 x 1)/100 + {(25000 â€“ A) x 8.5 x 1}/100 = 2031.25

=> 8A + 212500 - 8.5A = 203125

=> A= Rs 18750

Question 3 |

The simple interest and the true discount on a certain sum amount to same percentage. The interest and true discount amount to Rs. 25 and Rs. 20 respectively. The sum is?

Rs 500 | |

Rs 200 | |

Rs 250 | |

Rs 100 |

Question 3 Explanation:

Let A be the amount of money

And R be the rate percentage

Then Simple Interest

= (A x R )/100 = 25

=> A x R = 2500...................................................1

For true discount (discount percentage calculated on the actual selling price)

=> [(A â€“ 20) x R] /100 =20

=> (A x R -20R)/100 =20

=> AR â€“ 20R = 2000..............................................2

From eq. 1 and 2, we get

2500 â€“ 20R = 2000

R = 25%

Now eq.1

A x 25 = 2500 =>A= 100

And R be the rate percentage

Then Simple Interest

= (A x R )/100 = 25

=> A x R = 2500...................................................1

For true discount (discount percentage calculated on the actual selling price)

=> [(A â€“ 20) x R] /100 =20

=> (A x R -20R)/100 =20

=> AR â€“ 20R = 2000..............................................2

From eq. 1 and 2, we get

2500 â€“ 20R = 2000

R = 25%

Now eq.1

A x 25 = 2500 =>A= 100

Question 4 |

A trader owes a merchant Rs. 10028 due in 1 yr; but the trader wants to settle the account after 3 months.Â If the rate of interest is 12% per annum, how much cash should he pay?

Rs 9025 | |

Rs 9200 | |

Rs 9600 | |

Rs 9300 |

Question 4 Explanation:

Present value of money = v

ThenÂ Â (v x 12)/100 + v = 10028

=> (0.12v + v) = 10028

=> (v) = 10028/1.12

Now this amount will become after 3 months

[{(10028/1.12) x 12 x 3}/(12 x 100)] + 10028/1.12

=> {(10028 x 3) / 1.12 x100} + 10028/1.12

=> (10028/103)/ 112 = 9222.17 = Rs 9200

ThenÂ Â (v x 12)/100 + v = 10028

=> (0.12v + v) = 10028

=> (v) = 10028/1.12

Now this amount will become after 3 months

[{(10028/1.12) x 12 x 3}/(12 x 100)] + 10028/1.12

=> {(10028 x 3) / 1.12 x100} + 10028/1.12

=> (10028/103)/ 112 = 9222.17 = Rs 9200

Question 5 |

Sona invests an amount of Rs.9535 at the rate of 4% per annum, for how many years did she invest the amount to obtain the double her sum?

10 yr | |

25 yr | |

5 yr | |

4 yr |

Question 5 Explanation:

Let Sona invested for Y years

A sum will be double when interest is equal to principal

9535 = (9535 x 4 x Y)/100

4Y= 100

Y= 25 years

A sum will be double when interest is equal to principal

9535 = (9535 x 4 x Y)/100

4Y= 100

Y= 25 years

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